This dissertation consists of two topics: (1) structure-inspired disturbance observer design and (2) disturbance observer-based control/estimation. The disturbance is defined as the discrepancy between a model and the system the model represents. A disturbance observer is an algorithm that generates an estimate of the disturbance. The first topic illustrates a disturbance observer that provides a big class of nonlinear systems with a large basin of attraction, even ensuring global convergence. Such robustness is achieved by leveraging particular system nonlinearities in the observer design. The second topic discusses the usage of disturbance estimates to counteract or capture the effects of disturbances to recover the nominal controller/estimator performance. The main research results are theorems concerning stability analysis of the disturbance observer and the disturbance observer-based systems, whose practical aspects are supported by three application examples---a fixed-wing aircraft, an underwater vehicle, and a Furuta pendulum. / Doctor of Philosophy / This dissertation consists of two topics: (1) structure-inspired disturbance observer design and (2) disturbance observer-based control/estimation. Disturbances are the unknown signals entering the system; an external force, for example, such as the additional lift force due to turbulence surrounding an aircraft is a disturbance. A disturbance observer is an algorithm that estimates the mathematical value of disturbances. The first topic illustrates a disturbance observer whose convergence is guaranteed regardless of the initial condition. Such robustness is achieved by leveraging the system's special properties in the observer design. The second topic discusses the usage of disturbance observers to recover the nominal controller/estimator performance. Control is a study of how make systems behave ideally by properly designing the inputs, while estimation is about how to infer quantities that cannot be directly measured using the measurements that really are available; the solutions are correspondingly called controller and estimator. Disturbance estimates can be exploited by existing controllers and estimators as extra information to counteract or capture the effects of disturbances. The main research results are theorems about the conditions under which these algorithms perform as desired. Practical aspects are supported by three application examples---a fixed-wing aircraft, an underwater vehicle, and a Furuta pendulum.